Limit Point and Limit Circle Cases for Dynamic Equations on Time Scales

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References

1. Agarwal, R. P., Bohner, M. and Wong, P. J. Y. Sturm-Liouville eigenvalue problem on time scales, Appl. Math. Comput. 99, 153–166, 1999.
2. Akhiezer, N. I. The Classical Moment Problem and Some Related Questions in Analysis (Hafner, New York, 1965).
3. Amster, P., De Napoli, P. and Pinasco, J. P. Eigenvalue distribution of second-order dynamic equations on time scales considered as fractals, J. Math. Anal. Appl. 343, 573–584, 2008. [4] Amster, P., De Napoli, P. and Pinasco, J. P. Detailed asymptotic of eigenvalues on time scales, J. Diff. Equ. Appl. 15, 225–231, 2009.
4. Atici, F. M. and Guseinov, G. Sh. On Green’s functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math. 141, 75–99, 2002.
5. Bohner, M. and Guseinov, G. Sh. Improper integrals on time scales, Dynam. Systems Appl. 12, 45–65, 2003.
6. Bohner, M. and Peterson, A. Dynamic Equations on Time Scales: An Introduction with Applications(Birkh¨auser, Boston, 2001).
7. Bohner, M. and Peterson, A. (Eds.), Advances in Dynamic Equations on Time Scales (Birkh¨auser, Boston, 2003).
8. Chyan, C. J., Davis, J. M., Henderson, J. and Yin, W. K. C. Eigenvalue comparisons for differential equations on a maesure chain, Electronic Journal of Differential Equations 1998, 7pp., 1998.

9. Coddington, E. A. and Levinson, N. Theory of Ordinary Differential Equations (McGraw- Hill, New York, 1955).
10. Davidson, F. A. and Rynne, B. P. Global bifurcation on time scales, J. Math. Anal. Appl. 267, 345–360, 2002.
11. Davidson, F. A. and Rynne, B. P. Eigenfunction expansions in L2spaces for boundary value problems on time scales, J. Math. Anal. Appl. 335, 1038–1051, 2007.
12. Erbe, L. and Hilger, S. Sturmian theory on measure chains, Differential Equations and Dynamical Systems 1, 223–246, 1993.
13. Guseinov, G. Sh. Integration on time scales, J. Math. Anal. Appl. 285, 107–127, 2003.
14. Guseinov, G. Sh. Self-adjoint boundary value problems on time scales and symmetric Green’s functions, Turkish J. Math. 29, 365–380, 2005.
15. Guseinov, G. Sh. Eigenfunction expansions for a Sturm-Liouville problem on time scales, International Journal of Difference Equations 2, 93–104, 2007.
16. Guseinov, G. Sh. An expansion theorem for a Sturm-Liouville operator on semi-unbounded time scales, Advances in Dynamical Systems and Applications 3, 147–160, 2008.
17. Guseinov, G. Sh. Calculus and dynamic systems on time scales, In: A. Ma˘gden, editor, Pro- ceedings of the 20th National Symposium of Mathematics, Erzurum, Turkey (in Turkish), 1–29, 2009.
18. Hellinger, E. Zur Stieltjesschen Kettenbruchtheorie, Math. Ann. 86, 18–29, 1922.
19. Hilger, S. Analysis on measure chains–a unified approach to continuous and discrete calcu- lus, Results Math. 18, 18–56, 1990.
20. Huseynov, A. and Bairamov, E. On expansions in eigenfunctions for second order dynamic equations on time scales, Nonlinear Dynamics and Systems Theory 9, 77–88, 2009.
21. Putnam, C. R. On the spectra of certain boundary value problems, Amer. J. Math. 71, 109–111, 1949.
22. Titchmarsh, E. C. Eigenfunction Expansions Assosiated with Second-Order Differential Equations, Part I, 2nd ed.(Oxford University Press, Oxford, 1962).
23. Weyl, H. ¨Uber gew¨ohnliche Differentialgleichungen mit Singulrit¨aten und die zugeh¨origen Entwicklungen willk¨urlicher Funktionen, Math. Annalen 68, 220–269, 1910.
24. Yosida, K. Lectures on Differential and Integral Equations (Interscience, New York, 1960).